On black holes and d-branes

N=2 supersymmetric extreme black holes associated with the different types of the moduli space are investigated. The explicit solutions for the black hole entropy as a function of the electric and magnetic charges of the black hole are found. Starting with the simple case of two moduli and two electric and magnetic charges ( qΛ and p^ with Λ = 0,1) the investigation proceeds to the more complicated moduli spaces, such as the most general form of the Calabi-Yau moduli space with the arbitrary number of moduli fields. The global N=4 Supersymmetry transformations for the gauge-fixed K symmetric Born-Infeld D3 brane action are calculated in the fiat background using Killing gauge. One loop corrections to the effective Lagrangian for the D3 brane are found.